On $$\varGamma $$-Convergence of a Variational Model for Lithium-Ion Batteries
On $$\varGamma $$-Convergence of a Variational Model for Lithium-Ion Batteries
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关于 $$varGamma $$-锂离子电池变分模型的收敛性
DOI：
10.1007/s00205-020-01602-7
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发表时间：
2021
影响因子：
2.5
通讯作者：
Stinson, Kerrek
中科院分区：
文献类型：
--
作者：
Stinson, Kerrek
A singularly perturbed phase field model used to model lithium-ion batteries including chemical and elastic effects is considered. The underlying energy is given by $$\begin{aligned} I_\varepsilon [u,c ] := \int _{\varOmega }\left( \frac{1}{\varepsilon }f(c)+\varepsilon \Vert \nabla c\Vert ^2+\frac{1}{\varepsilon }{\mathbb {C}}(e(u)-ce_0):(e(u)-ce_0)\right) \, \mathrm{d}x, \end{aligned}$$wherefis a double well potential,is a symmetric positive definite fourth order tensor,cis the normalized lithium-ion density, anduis the material displacement. The integrand contains elements close to those in energy functionals arising in both the theory of fluid-fluid and solid-solid phase transitions. For a strictly star-shaped, Lipschitz domainit is proven thatwhereis finite only for pairs (u,c) such thatand the symmetrized gradientalmost everywhere. Furthermore,is characterized as the integral of an anisotropic interfacial energy density over sharp interfaces given by the jumpset ofc.
A singularly perturbed phase field model used to model lithium-ion batteries including chemical and elastic effects is considered. The underlying energy is given by $$\begin{aligned} I_\varepsilon [u,c ] := \int _{\varOmega }\left( \frac{1}{\varepsilon }f(c)+\varepsilon \Vert \nabla c\Vert ^2+\frac{1}{\varepsilon }{\mathbb {C}}(e(u)-ce_0):(e(u)-ce_0)\right) \, \mathrm{d}x, \end{aligned}$$wherefis a double well potential,is a symmetric positive definite fourth order tensor,cis the normalized lithium-ion density, anduis the material displacement. The integrand contains elements close to those in energy functionals arising in both the theory of fluid-fluid and solid-solid phase transitions. For a strictly star-shaped, Lipschitz domainit is proven thatwhereis finite only for pairs (u,c) such thatand the symmetrized gradientalmost everywhere. Furthermore,is characterized as the integral of an anisotropic interfacial energy density over sharp interfaces given by the jumpset ofc.
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